Equivariance and Canonicalization: 
A function \(\Gamma \)  over \(x\)  is said to be equivariant to a group operation \(\mathcal {O}\)  if its output changes by a fixed
mapping \(M\)  for any \(\mathcal {O}\)  operating on the input \(x\) , , \(\Gamma (\mathcal {O}x) = M(\mathcal {O}) \, \Gamma (x)\) .
In this paper, we are interested in equivariance to the \(SE(3)\)  group denoting 3D position and orientation (pose) – in particular we focus on the rotation group \(SO(3)\)  since 3D translation equivariance is readily achieved through mean centering [1]}.
Pose canonicalization is closely related to equivariance – our goal is to find an equivariant canonical 3D rigid transformation that maps the neural field of an object in arbitrary pose to a canonical pose.
We call the outputs of our method canonical fields – neural fields that are consistently oriented across a category of shapes.
